Leading critics of Britain's libel laws have said that the government's proposed reforms do not go far enough to prevent a "chilling effect" on freedom of speech. Physicist Brian Cox and comedians Dara O'Briain and Dave Gorman were among campaigners who delivered a petition, bearing more than 60,000 signatures, to Downing Street on Wednesday calling for greater changes to the public interest defence in libel cases.

Supporters of the Libel Reform Campaign, organised by Sense About Science and the Index on Censorship, also lobbied MPs over concerns about the lack of meaningful change in the Defamation Bill going through parliament, and how it would affect the reporting of science and health issues in the public interest.

The call comes a week after a young scientist was threatened with a libel action for posting a complaint he made to the General Medical Council, about a private GP, on Ben Goldacre's Bad Science website. Stuart Jones, a biochemist who raised the GP's use of unproven treatments, said of his ordeal: "What a horrible feeling it is to find yourself in this position after acting in what you believe is the public's interest."

Libel reform has been high on the agenda for some time, with all three major parties including plans for change in their manifestos. Nick Clegg has said, "this bill will be an international blueprint for freedom of speech."

However, critics are concerned that the bill doesn't include a defence of public interest for ordinary members of the public, nor measures to prevent companies suing individuals. "We face an inertia and, in science, the only way to meet that inertia is with force," said O'Briain.

Speaking during the lobby of parliament on Wednesday, several high-profile defendants of libel claims said that, according to their lawyers, the proposed changes wouldn't have helped their defence cases.

Also speaking at parliament was the science writer Ben Goldacre, whose exposure of Dr Matthias Rath in the Guardian resulted in a 17-month court case, which Rath eventually dropped. Rath was ordered to pay £220,000 in initial costs.

Despite winning their cases, Singh and Goldacre said the real concern was the number of journalists who had not written about important issues for fear of being threatened with legal action by big corporations – the "chilling effect" of libel laws.

Speakers also included representatives from the Mumsnet website, Which? magazine, and the Legal Beagles consumer blog, all of whom described instances where they had been threatened with libel actions for publishing content that they felt was in the public's interest.

David Marshall from Which? explained that when the magazine highlighted the behaviour of large corporations, rather than questioning the methodology, arguing their case and presenting their own evidence, there was a tendency for the companies to send a 9-10 page letter threatening legal action.

Conservative MP David Davis said: "Why should MPs have privilege to discuss evidence without fear of a libel action but not scientists? What we are after is to extend parliamentary privilege to those who offer a well-reasoned contribution to public discourse."

Cox said the robust, public critique of evidence was essential. "The idea that privilege is not extended to the public forum is, in my view, anti-democratic."

• This article was amended on 28 June 2012. The original cited the Legal Beagle blog as having been threatened with a libel action. This has been corrected.